Problem: Solve for $a$, $ -\dfrac{10}{2a - 4} = \dfrac{4}{10a - 20} - \dfrac{5a - 2}{2a - 4} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $2a - 4$ $10a - 20$ and $2a - 4$ The common denominator is $10a - 20$ To get $10a - 20$ in the denominator of the first term, multiply it by $\frac{5}{5}$ $ -\dfrac{10}{2a - 4} \times \dfrac{5}{5} = -\dfrac{50}{10a - 20} $ The denominator of the second term is already $10a - 20$ , so we don't need to change it. To get $10a - 20$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ -\dfrac{5a - 2}{2a - 4} \times \dfrac{5}{5} = -\dfrac{25a - 10}{10a - 20} $ This give us: $ -\dfrac{50}{10a - 20} = \dfrac{4}{10a - 20} - \dfrac{25a - 10}{10a - 20} $ If we multiply both sides of the equation by $10a - 20$ , we get: $ -50 = 4 - 25a + 10$ $ -50 = -25a + 14$ $ -64 = -25a $ $ a = \dfrac{64}{25}$